To solve the equation [tex]\((x-6) - (x+2) = 8x\)[/tex], let's go through the steps methodically.
1. Expand the equation:
[tex]\[
(x-6) - (x+2) = 8x
\][/tex]
2. Simplify the left-hand side:
Distribute the negative sign through the [tex]\((x + 2)\)[/tex]:
[tex]\[
x - 6 - x - 2 = 8x
\][/tex]
3. Combine like terms on the left-hand side:
The [tex]\(x\)[/tex] terms cancel out, and you are left with:
[tex]\[
-6 - 2 = -8
\][/tex]
Thus, the equation simplifies to:
[tex]\[
-8 = 8x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 8 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-8}{8}
\][/tex]
Simplifying this gives:
[tex]\[
x = -1
\][/tex]
Therefore, the solution to the equation [tex]\((x-6) - (x+2) = 8x\)[/tex] is [tex]\(x = -1\)[/tex].
Now, let's match this solution with the given multiple-choice answers:
- A. [tex]\(-1\)[/tex]
- B. [tex]\(2\)[/tex]
- C. [tex]\(8\)[/tex]
- D. [tex]\(7\)[/tex]
The correct answer is [tex]\(\boxed{A}\)[/tex].
